ENGR121 Engineering Mathematics Foundations Lecture Notes 2025 T2

These flashcards cover the key concepts from the ENGR121 Engineering Mathematics Foundations lecture notes, including definitions related to sets, functions, differentiation, series, and algebraic properties.

A set is defined as __.

any collection of objects, things, or states.

The notation Q represents __.

Rational Numbers which are of the form p/q where p and q are integers and q is nonzero.

In set theory, the symbol ∈ means __.

is a member of.

The union of sets A and B is written as __.

A ∪ B.

The process of finding the intersection of two sets A and B is indicated by __.

A ∩ B.

If the elements of A are also members of B, we say that A is a __ of B.

subset.

The complement of set A, denoted as __, includes all members of the universal set E that are not in A.

A¯.

The complement of a set is defined as the set of members of E that are __.

not in A.

In Boolean algebra, the OR operation is represented by the symbol __.

+.

The AND operation is represented mathematically by __ in Boolean algebra.

·.

The NOT operation is often referred to as __ in digital logic.

inverter.

The average rate of change of a function y(t) as t changes from t1 to t2 is given by __.

(y(t2) - y(t1)) / (t2 - t1).

The derivative of a function is defined as __.

the rate of change of that function.

If a function's derivative is positive, then the function is said to be __.

increasing.

The limits that define whether a derivative exists are checked by the __.

left-hand and right-hand limits.

The formula for the product rule in differentiation is expressed as __.

dy/dx = u dv/dx + v du/dx.

A geometric series can be expressed as __.

S = a + ar + ar² + … + ar^(k-1).

An arithmetic series is characterized by the general form __.

a, a + d, a + 2d, …

The Binomial Theorem can be formally stated as __.

(a + b)ⁿ = sum from k=0 to n of (n choose k) * a^(n-k) * b^k.

The basic properties of logarithms can help in understanding that __.

loga(bc) = loga(b) + log_a(c).

For the function f(x) = 2x, the derivative is __.

f'(x) = 2.